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Chan K I March 28, 2001 05:13

Viscous flow over an airfoil

I'm solving the 2-D compressible Navier-Stokes equations on unstructured grids for the NACA 0012 airfoil. The computational domain comprises the airfoil enclosed in a circular boundary.

I'm attempting to implement characteristic boundary conditions for the far-field. Would anyone know of suitable references which describe how this may be done?

Thanks very much.

Selina Tracy March 28, 2001 17:33

Re: Viscous flow over an airfoil
What's CHARACTERISTIC BC. Does it have something to do with hyperbolic equation, i mean, direction or speed of disturbances ..


Chan K I March 28, 2001 21:19

Re: Viscous flow over an airfoil
Hello Selina,

Based on what I know, characteristic BCs make use of information entering or leaving a boundary edge to adjust far-field conditions.

Appreciate it if there could be info on the details of implementation.


Guus Jacobs March 29, 2001 20:24

Re: Viscous flow over an airfoil
Try reading "Hirsch,C.", Numerical computation of internal and external flows, Vol. 2. It will explain the details of implementing characteristic boundary conditions for the Euler equations.

As for the implementation of characteristic boundary on the NS equations Poinsot and Lele extended the method described in the above reference for the Navier-Stokes equations in the following paper;

Boundary Conditions for Direct Simulations of Compressible Viscous Flows, Journal of Computational Physics 101, 104-129 (1992).

Hope that helps,


Chan K I March 29, 2001 21:26

Re: Viscous flow over an airfoil
Hello Guus,

Have read Chap. 19 of the book by Hirsch.

May I know if there are recent papers, as my library has JCP only from 1993 onwards.

Thanks very much, Chan K I

Guus Jacobs March 30, 2001 16:48

Re: Viscous flow over an airfoil
I would really try to get that paper, but if it is not possible, then the procedure comes down to writing the euler part of the NS equation in characteristic form. After that figure out the characteristic information on a boundary, which depends on the kind of boundary condition your using.

F.E. for an outflow boundary condition and subsonic flow there is one incoming characteristic which is lambda = u -c. Specifying the pressure one can find the amplitude of the disturbance along the incoming characteristic, with wich the Eulerian part of the NS equation is determined. The amplitudes along the outgoing characteristics are determined using the interior scheme.

The next step is to add the viscous terms of the NS equations to the eulerian part, find the unknown values using the interior scheme and integrate the NS eq. on the boundary in time together with the integration of the integration of the interior.

Again getting the paper saves a lot of time since the NS eq. are written in a form that can be used directly, whereas finding this form from Hirsch may be hard.


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